Magnetism and Matter

A bar magnet is modelled as an equivalent current-carrying solenoid: same external field shape, same torque/energy laws.

Falls as 1/r³, faster than a single pole’s 1/r², since opposite poles’ fields nearly cancel at large r.

Both give τ = 0. Only potential energy tells you which equilibrium is which:

1. θ = 0° (M ∥ B): U = −MB, a minimum. Nudge it and the torque restores θ → 0°. Stable.
2. θ = 180° (M antiparallel to B): U = +MB, a maximum. Nudge it and the torque grows, carrying it all the way to θ = 0°, never back. Unstable.
3. Rule: τ = 0 is necessary but not sufficient for stability — always check whether U is a minimum or a maximum nearby.

See it live: bar magnet simulation →

1. Declination: angle between geographic north and magnetic north (horizontal plane).
2. Inclination (dip): angle the total field makes with the horizontal; ≈0° at magnetic equator, ≈90° at magnetic poles.
3. Horizontal/vertical components: $H=B_E\cos(\text{dip})$, $Z=B_E\sin(\text{dip})$.

1. Diamagnetic: χ small and negative (~−10⁻⁵); weakly repelled. e.g. bismuth, copper, water.
2. Paramagnetic: χ small and positive (~10⁻³ to 10⁻⁵); weakly attracted; χ ∝ 1/T (Curie’s law). e.g. aluminium, sodium.
3. Ferromagnetic: χ large and positive (~10² to 10⁵); strongly attracted, can retain magnetisation. e.g. iron, cobalt, nickel. Becomes paramagnetic above its Curie temperature.